InterviewSolution
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InterviewSolution
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`(1-x^2)(dy)/(dx)+x y=a x` |
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Answer» Correct Answer - `y = a + c sqrt (1 - x ^(2))` ` (dy)/(dx) + (x)/(( 1- x ^(2))) *y = (ax)/((1-x ^(2)))` `IF = e ^(-(1)/(2) int (-2x)/((1 - x ^(2))) dx )= e ^(- (1)/(2) log (1 - x ^(2)) ) = (1)/(sqrt (1-x ^(2))` `therfore` Its solution is given by ` yxx(1)/(sqrt (1- x ^(2))) = int (1)/(sqrt (1- x ^(2))) xx (ax)/((1- x ^(2)))dx + C ` `" " = - (a)/(2) int (-2x )/((1 - x ^(2))^(3//2)) dx +C = - (a)/(2) int (dt)/(t^(3//2)) + C`, where ` (1- x ^(2)) = t ` `" " = - (a)/(2) int t^(-3//2) dt + C = (a)/(sqrtt) +C = (a)/(sqrt (1 - x ^(2))) +C ` |
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